He was named locally as Wayne Jones, said to be in his 50s, from Ebbw Vale in Blaenau Gwent, who was taken ill in a stand at Cardiff City Stadium.
A doctor who was in the crowd nearby tried to help the supporter, but was unable to save him.
Senior club figures have passed on their sympathies to Mr Jones' family.
In a statement on its website the club described Mr Jones as "a lifelong supporter".
"Mr Jones suffered a heart attack during the match against Leicester and was responded to initially by a fellow Cardiff City fan, a doctor who was in the area at the time," said the statement.